Monotone Iterative Scheme for Weakly Coupled System of Finite Difference Reaction-Diffusion Equations
by
D. B. Dhaigude
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad- 431004, INDIA
Coauthors: S. B. Kiwne, Department of Mathematics, Vinayakrao Patil Mahavidyalaya, Vaijapur Dist. Aurangabad, INDIA

The purpose of this paper is to develop monotone iteration scheme using the notion of upper and lower solutions for system of nonlinear finite difference equations, which corresponds, to the weakly coupled system of nonlinear reaction-diffusion equations with nonlinear boundary conditions. Two monotone sequences are constructed for the finite difference equations when both reaction function and boundary function are mixed quasimonotone. It is shown that these sequences converge monotonically to a solution of the finite difference system, which leads to existence-comparison result for the solution of the problem. Uniqueness of solution of the problem is also discussed.

Date received: February 17, 2007